Simplify the expression. $(5t^{4}-4t^{3}+3t^{2})(2t^{3}+3t^{2})$
Answer: First use the distributive property. $ 5 t^4 (2 t^3) + 5 t^4 (3 t^2) - 4 t^3 (2 t^3) - 4 t^3 (3 t^2) + 3 t^2 (2 t^3) + 3 t^2 (3 t^2) $ Simplify. $ 10t^{7} + 15t^{6} - 8t^{6} - 12t^{5} + 6t^{5} + 9t^{4} $ $10t^{7}+7t^{6}-6t^{5}+9t^{4}$ Identify like terms. $ { 10t^{7}} \color{#DF0030} {+ 15t^{6}} \color{#DF0030} {- 8t^{6}} {- 12t^{5}} {+ 6t^{5}} {+ 9t^{4}} $ Add the coefficients. $ { 10t^{7}} \color{#DF0030} {+ 7t^{6}} { -6t^{5}} {+ 9t^{4}} $